Question

Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with the given center and radius. (b) What is the intersection of this sphere with the yz-plane?

Answer 1

Answer: The equation of the sphere with the center and radius

`x^(2) +y^(2) +z^(2)-6 x+18 y-6 z+74=0`

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

`(x-h)^(2) +(y-k)^2+(z-l)^2 = r^2`

Given center of the sphere (3, -9, 3) and radius 5

`(x-3)^(2)+(y+9)^2+(z-3)^2 = 5^2`

on simplification , we get solution

`x^(2) -6 x+9+y^(2) +18 y+81+z^(2)-6 z+9=25`

`x^(2) +y^(2) +z^(2)-6 x+18 y-6 z+74=0`

Final answer :-

`x^(2) +y^(2) +z^(2)-6 x+18 y-6 z+74=0`

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

`y^(2) +z^(2)+18 y-6 z+74=0`